Support theorems on Rn and non-compact symmetric spaces

被引：0
|
作者：
Narayanan, E. K. [1 ]
Samanta, Amit [1 ]
机构：
[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 10期
关键词：
Support theorems; Paley-Wiener theorems; Analytic sets; Symmetric spaces; Spherical Fourier transform; DIFFERENTIAL-EQUATIONS; INFINITY;
D O I：
10.1016/j.jfa.2010.07.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider convolution equations of the type f * T = g, where f, g is an element of L-P (R-n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T, we show that f is compactly supported, provided g is. Similar results are proved for non-compact symmetric spaces as well. (C) 2010 Elsevier Inc. All rights reserved.
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页码：2587 / 2612
页数：26
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